The Holy Greek Orthodox Monastery of St Panteleimon is located on a side alleyway that runs off Khatsar Ma'ar Butrus St. The exact location is not clear in Google Maps but the alleyway is inside a small block of land used for private parking. There is a nun living in the Monastery who is very welcoming to pilgrims.
Link to google maps. This map is not accurate as the Gloria Hotel is not located so far up the road in reality and the side street before the monastery does not look like a street at all: HERE
Click photo to see larger image and longer description:
ST PANTELEIMON MONASTERY - JERUSALEM
Located behind a small private parking lot.
Entrance to Monastery. There is a door bell on the left next to the red door.
The nun lives alone and may not be available all of these hours. If nobody answers after you ring the doorbell, come back after an hour or the next day.
Approximate location. The street before does not actually look like a street in reality.